A new high accuracy finite difference discretization for the solution of 2D nonlinear biharmonic equations using coupled approach

DOI10.1002/NUM.20465zbMath1195.65147OpenAlexW1982001831MaRDI QIDQ3576823

Ranjan Kumar Mohanty

Publication date: 3 August 2010

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.20465

zbMATH Keywords

numerical examplesfinite differencesLaplacianhigh accuracymaximum absolute errorscompact approximationsuccessive tangential derivativestwo-dimensional nonlinear biharmonic equations

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Boundary value problems for higher-order elliptic equations (35J40) Error bounds for boundary value problems involving PDEs (65N15) Finite difference methods for boundary value problems involving PDEs (65N06)

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Uses Software

• KELLEY

Cites Work

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• Single cell discretizations of order two and four for biharmonic problems
• Multigrid solution of high order discretisation for three-dimensional biharmonic equation with Dirichlet boundary conditions of second kind
• Point and block SOR applied to a coupled set of difference equations
• Solution of the two dimensional second biharmonic equation with high‐order accuracy
• Difference methods of order two and four for systems of mildly nonlinear biharmonic problems of the second kind in two space dimensions
• Solving the Biharmonic Equation as Coupled Finite Difference Equations
• The Coupled Equation Approach to the Numerical Solution of the Biharmonic Equation by Finite Differences. II
• Block Five Diagonal Matrices and the Fast Numerical Solution of the Biharmonic Equation

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